The first thing I must say before I get started is that I couldn't have made and truly understood liquid soapmaking with out reading Catherine Failor's book Making Natural Liquid Soaps.  I strongly suggest buying this book and reading it over before attempting liquid soap.  The method I use on this page is her paste method which I find very easy to make.  The reason I am writing this web page is because I understand that when you are on a soap journey, the more information the better. 
Pat

The recipe
366 g coconut oil
1424 canola oil
400 g Potassium Hydroxide
1204 g water

This method uses a double boiler system, I use two pots, one
smaller than the other, the handles on the top pot hold it suspended over the bottom of the larger pot. I put water in the bottom one and when the top pot is on it, the water level is over the bottom of the top pot.

When you add the potassium hydroxide it will sound like it is going to explode or boil over, but the water does not bubble up at all and it doesn't even heat us as much as sodium hydroxide so don't worry.   
One more note, I am one of those risk taking soapers who doesn't even wear gloves when making soap. (this is not a recommended method of making soap!).  When mixing the water &  potassium hydroxide together and when mixing the soap there seems to be a very caustic steam that comes from the mixture.  When I make liquid soap I always wear long sleeves and gloves otherwise my skin begins to burn.   

-pre-heat the water in the bottom of your double boiler
- heat and mix your oils and fats like you normally would for cp, using the
temperatures 160 for the oils and 140 for the Potassium/water mixture, they will get to these temperatures very fast so be ready with your hot water in the bottom of your double boiler when you start. 

Try to bring your soap to trace, which even with a stick blender is pretty long.  It will go through a few stages before it hardens into your paste.  It will also keep trying to separate, but keep mixing it until it is VERY VERY thick like a very thick custard or maybe a meringue.   

Tip: Try to keep your soap as close to 160 deg as you can, if you go over 160 your soap will boil up over the top of the pot, much less than 160 and your soap will take forever to trace

This is not trace, just a good imitation.  It has to get much thicker than this.   If you stopped at this point your soap would separate.

Nope, this isn't it either, keep going.

I am not sure you can tell by this picture, but at some point your soap may look sort of grainy and like it is separating.  Keep going, this is normal. 

Now this is a stage you have to look out for.  This is what your soap looks like just before it starts to puff up and out of the pot.  What happens is that the soap gets too hot (you notice that it is in the double boiler.) and it doubles in size.

If you see this start happening get your pot into your sink and let it cool off.   I have a sprayer in my sink and I use it on cold and spray the outside of the pot.  I don't have any pictures of the soap puffing up, because I was just a tad too busy making sure I didn't get caustic soap all over the counter and the floor.  That is exactly what happened when I tried  a crockpot to make liquid soap.  I guess my crockpot is a bit too hot and there is no way to cool it down quickly as the sides are meant for insulation.  Catherine mentions this in her liquid soapmaking book, but she says that it is because of the trapped air in the soap.  Through my experience I disagree with her theory.  It does look as though it is full of air and that is why it is puffing up, but as long as the pot was too hot, I could not stir it down, while using a sprayer to cool the side of the pot immediately made the soap collapse back to it's original size.  Whatever the theory, be aware this may happen and be prepared.   

I didn't get a picture of the most important part of this process, trace, as when the soap came down from it's puffy stage it collapsed into a solid mass.  This is sort of what it looked like, but this is a bit further on in the process, after it has been heating for a while. 

Put the soap into the top of your double boiler and bring the heat up. It
will make a very stiff paste, I don't bother to try and mix it, it is far too thick.
Check your mixture twice for separation 20 min apart. You have to pry the paste away from the bottom of the pot. If it has separated there will be a clear liquid on the bottom. If you find this you will have to mix it up again, which believe me is not that easy, a very good reason to make sure you get it too full trace.